Max value

MBA.Aspirant wrote:3<a<b<c<14 ; 7<b<c<13 ; 8<c<10 ; the largest possible integer value of a+b+c is _______??

I think this one is confusing because he doesn't specify whether abc are integers.

So you could pick c = 9 or 9.9

b= 8 or 9.8

a= 7 or 9.3

a+b+c = 24
or a+b+c = 29

You are right that the fact that the variables are not integers is significant. However, he's not asking for the individual values of a, b, c, but rather asking for the greatest possible integer value of the sum. In other words, using this set of limitations, what's the largest sum you can come up that is still an integer?

Since we want the greatest total, we take a, b, and c to be as close to each other as possible. c has to be smaller than 10, and a and b need to be smaller than c, so we know that the total of a+b+c needs to be <10+10+10=30.
Can we make the next greatest integer = 29?
Take c=9.999, b=9.998, and a =9 + whatever decimal is needed to complement a and b to the next full integer (In the example above, a=9.003 will do, since .999+.998+0.003 will equal 2). The sum will equal 29, so THAT is the greatest possible integer value of the sum of a,b,c under these limitations.